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Homework Statement
Problem:
1C2 Let f(x) = (x  a)g(x). Use the definition of the derivative to calculate that f'(a) = g(a), assuming that g is continuous
Homework Equations
The Attempt at a Solution
I just started a self study of calculus using Khan and MIT OpenCourse. I am bit stuck, or maybe confused, with this exercise from MIT 18.01
The definition for the derivative is
[itex]\frac{Δy}{Δx}[/itex]=[itex]\frac{f(x)f(a)}{xa}[/itex]
I can replace f(x) with (xa)g(x), but I don't know what to do with f(a). In the given solution f(a) somehow becomes 0, but I can't see how.
The given solution:
Any help is much appreciated.
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